150g of ice is removed from a freezer at a temperature of -15°C. The ice is left, eventually reaching thermal equilibrium with its surroundings at a temperature of 21°C. If the latent heat of fusion for water is 336 kl/kg, the specific heat capacity of ice is 2100 J/kg.°C, and the specific heat capacity of water is 4200J/kg.°C, how much energy goes into the ice? Where does this energy come from?
q1 = heat added to raise T of ice @ -15 C to zero C.
q1 = mass ice x specific heat ice x (Tfinal - Tinitial) = ?
q1 = 0.150 kg x 2100 J/kg x [0 -(-15)] = ?
q2 = heat added to convert solid ice to liquid water.
q2 = mass H2O x heat fusion ice @ zero C.
q2 = 0.150 kg x 336 kJ/kg = ?
q3 = heat added to raise T of liquid water from zero C to 21 C
q3 = mass H2O x specific heat H2O x (Tfinal - Tinitial)
q3 = 0.150 kg x 4.2 kJ/kg x (21 - 0) = ?
Totol Q = q1 + q2 + q3
Post your work if you get stuck.
To find the amount of energy that goes into the ice, we need to calculate the energy required to heat the ice from -15°C to 0°C, and then the energy required to melt the ice at 0°C to water at 0°C, and finally, the energy required to heat the water from 0°C to 21°C.
Let's break down each step and calculate the energy required:
Step 1: Energy to heat the ice from -15°C to 0°C
The specific heat capacity of ice is given as 2100 J/kg.°C.
The temperature change is 0°C - (-15°C) = 15°C.
So the energy required to heat 1 kg of ice is: 2100 J/kg.°C * 15°C = 31,500 J.
Since we have 150g of ice, which is equal to 0.15 kg, we can calculate the energy required for this step as follows:
Energy = 31,500 J/kg * 0.15 kg = 4,725 J.
Step 2: Energy to melt the ice at 0°C to water at 0°C
The latent heat of fusion for water is given as 336 kJ/kg.
Since 1 kJ = 1000 J, the latent heat of fusion is 336 kJ/kg * 1000 J/kJ = 336,000 J/kg.
The energy required to melt the 0.15 kg of ice is: 336,000 J/kg * 0.15 kg = 50,400 J.
Step 3: Energy to heat the water from 0°C to 21°C
The specific heat capacity of water is given as 4200 J/kg.°C.
The temperature change is 21°C - 0°C = 21°C.
The energy required to heat 1 kg of water is: 4200 J/kg.°C * 21°C = 88,200 J.
Since we have 0.15 kg of water now, we can calculate the energy required for this step as follows:
Energy = 88200 J/kg * 0.15 kg = 13,230 J.
Total Energy:
The total energy required is the sum of energy for each step:
Total Energy = Energy step 1 + Energy step 2 + Energy step 3
Total Energy = 4725 J + 50400 J + 13230 J
Total Energy = 68,355 J
Therefore, the amount of energy that goes into the ice is 68,355 J.
Now, as for where this energy comes from, it depends on the context. In a freezer, the energy may come from the electricity powering the freezer, which is then converted into cooling. In other cases, the energy could come from an external source like heat in the surrounding environment or a heater or heating element.